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Hankel operators on the weighted Bergman spaces with exponential type weights

Authors:	Peng Lin Richard Rochberg

Institution:	(1) Department of Mathematics, Washington University, Campus Box 1146, 63130 St. Louis, Mo, USA

Abstract:	Let $AL_\varphi ^2 \left( \mathbb{D} \right)$ denote the closed subspace of $L^2 \left( {\mathbb{D},e^{ - 2\varphi } dA} \right)$ consisting of analytic functions in the unit disk $\mathbb{D}$ . For certain class of subharmonic $\varphi :\mathbb{D} \to \mathbb{Z}$ , the Hankel operatorH _b on $AL_\varphi ^2 \left( \mathbb{D} \right)$ with symbol $b \in L^2 \left( \mathbb{D} \right)$ is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation.

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